An algorithm for monotropic piecewise quadratic programming is developed. It converges to an exact solution in finitely many iterations and can be thought of as an extension of the simplex method for convex programming and the active set method for quadratic programming. Computational results show that solving a piecewise quadratic program is not much harder than solving a quadratic program of ...

The problem of minimizing f̃ = f +p over some convex subset of a Euclidean space is investigated, where f(x) = x Ax + b x is a strictly convex quadratic function and |p| is only assumed to be bounded by some positive number s. It is shown that the function f̃ is strictly outer γ-convex for any γ > γ∗, where γ∗ is determined by s and the smallest eigenvalue of A. As consequence, a γ∗-local minimal...

Applying an interior-point method to the central-path conditions is a widely used approach for solving quadratic programs. Reformulating these in log-domain natural variation on this that our knowledge previously unstudied. In paper, we analyze methods and prove their polynomial-time convergence. We also they are approximated by classical barrier precise sense provide simple computational exper...

The Quadratic Convex Reformulation (QCR) method is used to solve quadratic unconstrained binary optimization problems. In this method, the semidefinite relaxation is used to reformulate it to a convex binary quadratic program which is solved using mixed integer quadratic programming solvers. We extend this method to random quadratic unconstrained binary optimization problems. We develop a Penal...